8-1 and 8-2 Polynomial Review

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. It can be expressed in the form: a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 4x^3 + 2x^2 - x + 7, the degree is 3.

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How do you factor a polynomial?

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To factor a polynomial, you express it as a product of its factors. This can involve finding common factors, using special factoring formulas (like difference of squares), or applying methods such as grouping.

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What is a monomial?

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A monomial is a polynomial with only one term. For example, 5x^2 is a monomial.

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What is a binomial?

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A binomial is a polynomial with exactly two terms. For example, 3x + 4 is a binomial.

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What is a trinomial?

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A trinomial is a polynomial with exactly three terms. For example, x^2 + 5x + 6 is a trinomial.

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What is the difference between a polynomial and a monomial?

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A polynomial can have multiple terms, while a monomial has only one term. For example, 2x + 3 is a polynomial, while 4x^2 is a monomial.

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What does it mean to simplify a polynomial expression?

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Simplifying a polynomial expression means combining like terms to reduce it to its simplest form. For example, 3x^2 + 2x^2 simplifies to 5x^2.

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What is the process of adding polynomials?

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To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5) = 6x^2 + 5x + 5.

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What is the process of subtracting polynomials?

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To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 + 3) - (2x^2 + 1) = 3x^2 + 2.